He was drafted by the club in the 8th round of the 2011 amateur draft after two excellent years at Texas State University. In 2010, he was 10-4 with a 3.10 ERA in 24 games (13 starts) and in 2011, he was 9-3 with a 1.99 ERA in 17 games (15 starts). In 113 1/3, he had 129 strikeouts.

The pitcher climbed through the Mariners' minor league ranks quickly. In 2012, he pitched for the High-A High Desert Mavericks and went 5-1 with 15 saves and a 2.90 ERA in 49 games. He struck out 77 batters in 62 innings. In 2013, the pitcher had 15 saves and a 1.80 ERA in 44 games for the Double-A Jackson Generals, striking out 71 batters in 50 innings. He was named a MiLB.com Organization All-Star following the campaign. Smith began 2014 with the Triple-A Tacoma Rainiers. He went 1-3, 2.93 with 10 saves in 39 games to earn a September call-up to Seattle, where he made his debut on September 1st. He made 9 appearances for the M's, winning one game and not allowing a run in 8 1/3 innings. That good work earned his a spot in the team's bullpen at the start of 2015 and he had a very solid rookie season. In 70 games, he went 2-5, 2.31, with 92 strikeouts in 70 innings, and earned 13 saves after taking over as the team's closer when Fernando Rodney struggled in the role. On December 7th, he was traded to the Boston Red Sox along with Roenis Elias in return for Ps Jonathan Aro and Wade Miley. In Boston, he was on tap to be main set-up man for newly acquired closer Craig Kimbrel.